Zero-energy states in corrugated bilayer graphene

Abstract

Anomalous quantum Hall effects in single-layer and bilayer graphene are related with nontrivial topological properties of electron states (Berry phases $\pi$ and 2$\pi$, respectively). It was known that the Atiyah-Singer index theorem guarantees, for the case of the single-layer, existence of zero-energy states for the case of inhomogeneous magnetic fields assuming that the total flux is non-zero. This leads, in particular, to appearance of midgap states in corrugated graphene and topologically protects zero-energy Landau level in corrugated single-layer graphene. Here we apply this theorem to the case of bilayer graphene and prove the existence of zero-energy modes for this case.Comment: minor changes (misprints are fixed, a bit more explanations in the mathematical part are added

Quantum Transport and Field-Induced Insulating States in Bilayer Graphene pnp Junctions

“…This excellent agreement between VRH model and our data strongly suggests a successful band gap opening in BLG, and transport via variable range hopping between localized states that either lie within the gap [29][30][31][32] or are formed from disorder-induced charge puddles 33,34 .…”

Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture

“…In unperturbed graphene all Landau levels have a twofold valley degeneracy 9 The absence of a splitting of the zeroth Landau level can be understood as a topological protection in the context of an index theorem [18][19][20][21], which requires that either i =0.1, f=0, ν=1). The data points are calculated numerically [22] from the tight-binding Hamiltonian (1) with bond modulation (4).…”

External gates and transport in biased bilayer graphene

“…Also notable in these systems is a Berry phase of 2 accompanying an unconventional quantum Hall effect 6 and predictions of Andreev reflection 7 and superfluidity 8 among other effects. [9][10][11][12][13][14][15][16][17] Studies of graphene bilayers have focused on transport, [18][19][20][21][22][23][24][25][26][27] compressibility, 28 impurities, [29][30][31] electron-electron interactions, [32][33][34][35] and band and electronic structures. [36][37][38][39][40][41] Graphene bilayers are interesting from a physics point of view because they are not merely the sum of two layers.…”